Do pet birds get avian flu like chickens do ?

I was just reading that in India, and somewhere else that I have forgotten, they are killing thousands of chickens. They have found chickens that had avian flu, and it is possibly the kind that can spread to humans, so they are killing the chickens to prevent the flu from spreading.
The interesting part is that they think that the chickens got the avian flu from wild birds flying into the area and transmitting the flu to the chickens.
So, what I have been wondering , is if the flu originally came from wild birds, could it also spread to pet birds like canaries and parakeets ? ?
It would seem to me that if it can spread from a wild bird to a domestic chicken, that it could also spread to someone's pet bird, and then to the owner of the bird, since it is the variety of avian flu that is contagious to humans.